Mailbag: Retirement Projections, Monte Carlo Software, And Longevity Assumptions For Retirees

Posted by Michael Kitces on Thursday, March 13th, 7:01 am, 2014 in MailBag

Many readers of this blog contact me directly with questions and comments. While often the responses are very specific to a particular circumstance, occasionally the subject matter is general enough that it might be of interest to others as well. Accordingly, I will occasionally post a new "MailBag" article, presenting the question or comment (on a strictly anonymous basis!) and my response, in the hopes that the discussion may be useful food for thought.

In this week's MailBag, we look at some issues with Monte Carlo retirement plan projections, cash-flow versus goal-based planning software, and the appropriateness of using arbitrary-age life expectancy assumptions (e.g., all clients assumed to live to age 95) versus more client-specific or entirely randomized life expectancy in the Monte Carlo projection.


Question/Comment:  What I'd like to do is have you confirm some "assumptions" for me that I've been able to glean (I think, it could be my own confirmation bias at work here) from your writings and others you've collaborated with on Monte Carlo, Risk Capacity, etc.  

First of all, am I correct in my assumption that it is, in your opinion, more pragmatically correct to "randomize" life expectancy in the application of Monte Carlo Simulations. My recollection from one of your papers was that pegging retirement to a specific "age" effectively narrows and constrains the MCS assumptions to a very narrow range. As an example, we used Vanguard mortality estimator for a Client plan just the other day; our Client is 68 years old and according to the Vanguard mortality numbers, our 68 year old only as a 20% chance of living to age 90. My argument is then that running a MCS report based on age 90 would effectively only be looking at 20% of the possible outcomes. Is that right?

I have to admit, this is an area where I am still a bit torn myself.

Your latter comment here is correct; strictly speaking, “forcing” life expectancy to age 90 narrows us to only 20% of scenarios where a client even survives that long. Which means a plan that “only” has a 95% probability of success and a 5% chance of failure actually has something more like a 99% probability of success and only a 1% chance of failure, because there’s only a 20% chance that the client will even survive for the 5% adverse scenarios.

Accordingly, I think randomizing life expectancy is a good solution, but only if the standards for success are adjusted appropriately. The concern is that, given the shape of the mortality curve, with a rare but long tail, using randomized mortality is essentially going to give the client more latitude to spend heavily for the 80% of scenarios he/she won’t live to 90, in exchange for what may be massive catastrophes for outliving it. The outcomes are very asymmetric; often, you can spend slightly more (since "most of the time" longevity falls short of age 90), but in the subset of scenarios you’re not dead, you may be “very” broke due to the compounding depletion of assets. Which is a nice way of saying that perhaps the ‘arbitrary’ long time horizon is perhaps quite conservative, but not necessarily a ‘ludicrous’ approach. Still, this generally can be resolved by using randomized mortality with a relatively high standard for success.

In other words, you might tackle this by “forcing” life expectancy to age 90 or 95 but requiring a “moderate” probability of success (85%? 90%?) given that these are relatively unlikely survival points in the first place (it there's only a 20% chance OF that 10%-15% failure which means the real failure rate is only 2-3%%!), or you could use randomized mortality but set a higher standard for success (95%? 97%?). Mathematically, you can set the joint probabilities to be roughly the same, where a 95% probability at arbitrary age 90 (shown as joint probability of 99% above) is the same as a 99% probability with randomized mortality (not quite identical because the shape of the randomized mortality curve is still different than an arbitrary-to-age-95-then-a-cliff alternative, but close enough under the circumstances).

So I guess in essence, the point is that I think randomized life expectancy is probably best from the theoretical framework, but only if you properly adjust your standards for success and failure. In practice, I’m not sure most advisors can/would do this properly (in general, most are ‘undertrained’ on Monte Carlo in my opinion), and I don’t think that arbitrary mortality is a terrible substitute in such circumstances. However, I also worry that advisor undertraining means we’re making plans that are excessively conservative as well; I get it from our end (no planner wants to be the one who has clients running out of money on their watch), but it does ‘inflict’ our professional conservatism on our clients lives in a significant (and not always positive) manner.

That aside, it’s also worth noting that, as I've written recently, I fear most planners fail to appreciate the significant differences between individual and joint mortality. Doing projections for individuals and married couples to the same age appears fairly common (these days, it seems like most advisors I see are doing projections to an arbitrary age of 95 regardless of whether it's an individual or couple), yet the reality is that a SINGLE life expectancy to age 95 is drastically less likely than a JOINT life expectancy to age 95, and the life expectancy of BOTH members of the couple being alive at age 95 is significantly different than just one being alive (with different spending implications). I fear we gloss over these distinctions too often; one upshot to randomized mortality built into the tool is that, in essence, it puts these calculations directly into the software and avoids these “user errors in assumptions” professional issues.

Question/Comment:  My software company advises I should strive to reach 100% MCS probability outcomes. My recollection from various readings, most notably yours, is that a 100% outcome is not necessary and is not necessarily optimal. My sense is that the fear of striving for a 100% outcome is problematic from two perspectives, namely; [1] it unduly constrains spending early in retirement and [b] likely results in Clients "under spending" during their retirement years only to realize at the far end that much to much money will be left and the resulting likelihood that retirees might be in too poor health or simply too old to now rejigger spending and really enjoy retirement to it's fullest. Is that correct? (Note: we do strive to have MCS results higher than a range of 86% to 93% wherein a Client states a specific legacy goal. Many, if not most, do not specify such a goal.)

Indeed, I am most definitely NOT a fan of trying for 100% Monte Carlo probability outcomes. They are unduly harsh and constraining; in the real world, to assume as a “default” that all clients will live well past age 100 (necessary to really ensure 100% probabilities of success) is just not appropriate as a baseline. It severely constrains spending when it will not be relevant in virtually all scenarios (by definition), and in practice I rarely see clients who want to plan this way anyway (there are a handful of ‘longevity-fearers’ but they’re certainly not the ‘default’).

From the practical perspective, the bigger issue here is that to frame things as 100% probabilities of success (and aiming for 0% probabilities of failure) is a misstatement of the actual outcomes. A probability of success is really a probability of EXCESS – as it defines a threshold where the client finishes with that much money, OR ANY EXCESS ABOVE THAT AMOUNT, as an outcome; to characterize all outcomes as being “equivalent” successes regardless of whether the client finishes with $1 or $10,000,000 does a disservice to clients in my opinion, as while few want to cut it so close as finishing with $1, few want to die with $10,000,000 either, and it’s rare that clients view a $1 or $10,000,000 legacy as being equivalent, even though that’s the result of aiming for a 100% probability of success (without looking at the magnitudes of excesses that entails).

Similarly, probability of failure is a misstatement in my view as well. It’s rare that clients spend themselves off a cliff until one day they wake up and all the checks are bouncing. In practice, most clients at some point realize that their assets are depleting and begin to adjust. The later the adjustment, the more severe it has to be to get back on track, but it certainly can be done (though preparing clients for adjustments and coaching them through it is clearly something we could be better trained to do and explain to clients).

Yet when it’s framed from this perspective for clients, the decisions are quite different. To state a client has a 90% probability of success and a 10% probability of failure sounds scary. To say the client has a 90% probability of leaving behind an inheritance, which have the time will be several million dollars, while there’s a 10% probability that they will need to apply a modest mid-course adjustment that might necessitate cutting spending by 5%-10% for a couple of years, feels entirely different. The latter framing may be quite palatable – and in fact, preferable – for the client. The former sounds terrifying (10% probability of eating dog food living under a bridge!?). Yet these are actually the same scenarios, just explained with different words and context.

Question/Comment: Lower estimated MCS results might be more beneficial than higher ones in scenarios where the possible downside/recovery time for a portfolio consumes an extended period of retirement time. I wrote a spreadsheet/graphic to depict what I think you had advanced in one of your writings, wherein, during the "event horizon" (I think Black Hole terminology is prescient here) we can see the recovery period of a back-to-back "black swan" (ok, "merely random event") over time. As an example, we have an actual Client whose goal is to spend his retirement time and money building lasting and loving family relationships. This would involve using his resources to pay for family travel to his new retirement home in Georgia, but he wants to spend that money assuring that no less than 10 family members can fly in to Georgia from around the country to spend [a] a summer vacation, [b] Thanksgiving and [c] Christmas all together in my Client's mountain cabin. To get a MCS result higher into the 90% range, we'd have to hold more equities than we do now. A back to back substantive drop in market value leaves a recovery time of almost the Client's entire retirement time horizon. A lower allocation to equities, in the 60% range, shortens recovery times considerably. My Client opted for the lower MCS and allocation to equities on the predicate that; "I'd be apprehensive about spending that money each year to bring everyone together if the value of my assets were underwater for such an extended period..." Is this a philosophy rooted in sound thinking on my part?

This is an interesting way to frame the issue.

Certainly, I do think it’s valid to choose outcomes that have a lower “probability of success” that also entail less volatility – not necessarily because of the different recovery period, per se, but because they result in “less” of a catastrophe. With the lower equity exposure, there might be a 10% chance of ‘adjustment’ (e.g., must reduce lifestyle a little, or maybe mortgage the Georgia cabin); with the higher equity exposure, the probability of adjustment might be only 5%, but if the adjustment has to occur, it will be a requirement to SELL the cabin. The probability of ‘failure’/adjustment is lower, but the failure/adjustment is more severe. In such circumstances, choosing the higher likelihood of adjustment that is a more modest adjustment is entirely rational.

Indirectly, if the client’s goal is “preserve principal for inheritance” the conclusion is basically the same with the wording you used – the ‘magnitude of failure’ is how far underwater the client might be for an extended period of time before recovering. But from the overall sustainability perspective, it’s not just about “how long until recovery” but about “the danger you draw down so far your ongoing spending depletes the portfolio before you EVER recover”. Bear in mind that the real issue here is not short-term “black swan” bear markets, but extended periods of time with substandard market returns. In other words, it’s not about the 40% market crash (where one year’s worth of withdrawals aren’t really material anyway); it’s about the scenario where the market has no appreciation for a decade (an extended period of 'mediocre' returns), while ongoing withdrawals are occurring (which add up to serious ‘damage’ over a decade).

Question/Comment: In your recent work with Pfau, are you guys saying that a bucket strategy works best (mathematically) when the cash/bonds buckets are spent down and not replenished from an equity component and then by design, the Client is left with only that equity component as the remaining asset pool to draw from?

Yes, that’s basically the point from the rising equity glidepath paper we did.

Strictly speaking, the recommendation wasn’t actually to spend the bonds down ENTIRELY and leaving only equities; that would essentially be a glidepath that finishes with 100% in equities, which is a bit extreme (though it’s a helpful way to explain the framework). The better scenario was where “most” but not “all” spending occurred from the bond bucket, such that the portfolio didn’t glide all the way up to 100% in equities, but perhaps from 30% in equities up to “only” 60% or 70% in equities.

Technically, you can accomplish this by just doing annual rebalancing every year, but instead of rebalancing the client to 30/70 each year, you rebalance to 30/70, then 31/69, then 32/68, then 33/67, etc. Mathematically, this would be the equity of spending more (but not all) of your money from the bond bucket each year WITHOUT replenishing it (which slowly liquidates the bond bucket while the equities grow and become a larger percentage).

But ultimately, the bucket mechanism was explanatory; the rebalancing methodology was how we actually did the research. You could create a bucket strategy that effectively replicates this, and what you’d end out with is a bucket strategy that disproportionately spends from the bonds and does not replenish them (causing equity exposure to rise over time).

Question/Comment: Is there any research into how long the "cash/bond" bucket pool should exist as a means of supplementing in Item 4 above?

Not specifically. In the context of our research, we did test various sizes of starting and ending stock/bond allocations. But we did not test difference “paces” of spenddowns, like aiming to glide to the target equity exposure in 10 or 15 years instead of 30 (which would effectively spend down the cash/bond bucket pool quicker or more slowly).

Bear in mind as well that technically, having cash/bond buckets to “avoid liquidating bonds in bear markets” are technically not necessary nor advantageous anyway; the reality is that simple rebalancing actually accomplishes the goal. That’s why we ultimately tested a series of rebalancing strategies with varying glidepaths, as opposed to literally testing them as bucket strategies. The bucket mechanism is effective for explanatory purposes, but strictly implemented can actually distort asset allocation and end out with inferior outcomes.

Question/Comment: As you know there are certain "cash flow" based planning applications out there, Navi Plan is one to be sure. I was an IFS user back in the 80's so as Harold Evensky often "chides" me, "you're a cash flow junky..."  That being both said and true, is it not more "effective" to be projecting actual Client cash flows (assuming that the plan goes through frequent updates) than it is to make the assumption that retirement spending will be either [a] a function limited by a percentage of the Clients pre-retirement income or; [b] pre-retirement spending? 

The “goal based” programs (as opposed to “cash flow based”) go FAR deeper than just projecting a percentage of client pre-retirement income or spending. You can precisely calculate what you want the exact targeted retirement spending to be, and insert additional ‘goals’ for irregular cash flows (spend an extra $20k on travel in your 60s, put aside $50k for grandchild’s education, sell the vacation cabin when you’re 85, etc.). The primary difference between cash-flow and goal-based planning is the level of detail, and especially during the accumulation years what happens with excess cash flow (a cash-flow-based package generally tracks all income, nets spending, and assumes the rest is saved, while a goal-based package “only” saves what it is specifically told to save as a goal/target). Goal-based programs also tend to make more flat and generalized assumptions regarding tax rates, rather than doing a detailed year-by-year tax projection.

Certainly, the ‘cash flow junkies’ as Harold calls you often prefer this level of year-by-year cash flow detail. The cash flow critics generally suggest that the problem is a cash flow projection mistakes precision for accuracy; doing a 30-year retirement projection assuming the client spends $129,475 in the 30th year instead of “roughly” $130,000 (or assuming returns of 8.12853% instead of just 8%) may be more precise of a projection, but it’s not necessarily more accurate, given the incredible amount of change that can (and is likely?) to occur over the next 30 years anyway and the uncertainty of exactly estimating the inputs anyway.

This acknowledgement – that greater precision only brings limited improvements in accuracy – and the flexibility of goal-based packages today, is why most of the growth has been in goal-based packages over cash-flow-based, and in practice the two are heavily converging towards each other anyway. I don’t know if we’re there yet, but we’re arguably getting pretty close to the point where the differences between what can be done in cash-flow-based packages vs goal-based solutions are increasingly about precision that doesn’t necessarily make the projection more accurate because the uncertainty of the overall time horizon is so extreme already.

Question/Comment: Do you support, in theory at least, Zvie Bodie's concept of "flooring" with the understanding that I'm asking about either [a] is creating additional "flooring" via annuitization wise beyond where flooring may already exist (Social Security, pension, RMD, etc.) and/or [b] is it wise to create flooring where none exists with the exception of Social Security and RMD's? (I'm not even sure that's a legitimate question, but I think that you get my point)

I view the flooring concept as being entirely valid and appropriate; the caveat is that I see safe withdrawal rate strategies AS flooring strategies. The academics are fans of doing this via annuitization (or laddered TIPS), but using annuitization or TIPS strategies is just one way TO set up a floor, and arguably a much less flexible one, with upside (in the case of annuitization) in only a small subset of cases where clients truly live materially beyond their life expectancy. Not that I’m anti-annuity – my first book was actually the Advisor’s Guide To Annuities and we're still updating it! – but I do find the Bodie/academic case to ‘overstate’ annuities to the exclusion of other alternatives (like portfolio-based strategies with prudent conservative spending set as a floor, which essentially is what the safe withdrawal rate approach embodies).

In other words, given that safe withdrawal rates have a 96% chance of leaving 100% of starting principal, and a median outcome of more-than-quadrupling wealth, it arguably sets a very sturdy floor already! Yes, there is still a potential for “black swan” style events that can disrupt it, but the reality is that black swans can disrupt insurance companies as well; in fact, given that the scenarios which cause insurance companies to fail are often themselves black swans, arguably using insurance companies to ‘hedge’ black swans is actually a rather ineffective method of doing so, as the black swan scenarios of markets and insurance companies are highly correlated.

So as I'd view it, setting a floor using SWR versus a floor using Social Security, a pension, or annuitization, are just different mechanisms FOR setting a floor, and they each have their own costs, benefits, advantages, and disadvantages (though strictly speaking, delaying Social Security is basically the most favorably priced of them all in today’s marketplace!). On the other hand, it’s worth noting that RMDs are not a flooring strategy at all; they’re simply a tax requirement to move money from bucket A (the IRA) to bucket B (the brokerage account). Whether the client spends the money is their call. And because RMDs are recalculated annually – on a volatile account balance – they’re actually a very weak flooring mechanism, as a market decline produces a similar drop in the recalculated RMD and therefore a remarkably unstable floor.

I hope that helps a little as some food for thought!


One Pingback/Trackback

Blog Updates by Email

Nerd’s Eye View Praise

@MichaelKitces Twitter


Out and About

Thursday, September 25th, 2014

Should Equities Decline in Retirement, Or Is A Rising Equity Glidepath Actually Best? @ FPA Houston

Tuesday, September 30th, 2014

Future of Financial Planning in the Digital Age Setting a Proper Asset Allocation Glidepath in Retirement @ Society of Financial Service Professionals

Wednesday, October 1st, 2014

Setting  A Proper Asset Allocation Glidepath in Retirement Cutting Edge Tax Planning Developments & Opportunities @ FPA San Diego

VIEW FULL SCHEDULE